Thermal runaways in batch processes can lead to significant issues for safety and performance during normal operation in industry. This is usually circumvented by running such processes at lower temperatures than necessary, hence losing the opportunity to intensify production and therefore reduce reaction time. The detection of the thermal. stability of batch systems can potentially be embedded in an advanced control scheme, therefore improving the performance by being able to intensify the process, achieving higher yields while keeping a stable operation. The derivation of stability criterion K for high-order reactions is presented in this work, resulting in better control when embedded in Model Predictive Control (MPC) schemes than standard nonlinear MPC schemes, based on the work in Kahm and Vassiliadis (2018). The non-trivial extension of stability criterion K for multi-component reactions with application to MPC systems is discussed in detail. The logic and verification of the form of the resultant Damkohler number in particular is discussed and demonstrated with case studies. A comparison of various MPC schemes is presented, showcasing that the implementation using criterion K results in intensified processes kept stable at all times, whilst reducing computational cost with regard to standard nonlinear MPC schemes. Furthermore, reaction times are reduced by at least twofold with respect to processes run at constant temperatures. (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.